I'm going to work from a different set of numbers, but reach the same conclusion.
Octopus tells me we used 800kWh in August and 2000kWh in December. To a first approximation, we're using 1200kWh/month, or 40kWh/day, to heat the house. (Most houses will do better than this: ours is both big and old.)
I'll pick on a region for which I can find data: London gets 0.52kWh/m² of solar energy a day.
https://en.wikipedia.org/wiki/Solar_power_in_the_United_Kingdom
#SolarPanels are roughly 20% efficient, and you lose a bit in the inverter, the cables and the battery system, so let's say you can extract 0.1kWh/m² per day, and your #HeatPump boosts that to, I don't know, 0.25kWh/m² per day. (The COP, as you know, is lowest when it's coldest.) So we'd need 160m² of solar panels to heat our house from the sun in December. No one has the space or the budget for that.
On the bright side, since we installed heat pumps, we've gone from burning logs most evenings to maybe once a week.
